On frequency comb formation in terahertz quantum cascade lasers

Their inherently broadband gain and high value of the third order nonlinearity makes quantum cascade lasers (QCLs) ideal candidates for frequency comb generation in the terahertz (THz) and mid-infrared (midIR) spectral ranges. In recent years, it has been demonstrated that free running QCLs can produce broad comb spectra, even without any special endeavour to induce phase-locking of the lasing modes [1]. Unfortunately, such “coherent” regimes of multimode operation seem to span only a very narrow portion of the full dynamic range of the devices, which hinders the practical usability of this technology [1, 2]. Group velocity dispersion (GVD) has been largely considered as the main comb degradation mechanism, due to the variation in the cavity-mode spacing it introduces. As a consequence, special dispersion compensation mechanisms (DCMs) were developed to suppress this effect, however again with variable success [2,3]. In a recent publication [4], the formation of a population grating due to the interference of counter-propagating waves, commonly referred to as spatial hole burning (SHB), together with four-wave mixing (FWM) arising from the third-order optical nonlinearity, have been identified as the main mode-proliferation processes in QCLs. While the former has been shown to produce a broad and dense, but incoherent spectrum, the latter effect is argued to homogenize the spacing and introduce phase-locking in the lasing modes. Individually, these mechanisms have been well understood, but when considered together, the complex dynamics becomes difficult to analyse. Based on the numerical solution of the multi-level Maxwell-Bloch equations, we investigate how the interplay between GVD, SHB and FWM determines the comb formation. In [5], we outlined a theoretical model for the full time-domain simulation of THz QCLs, and showed that it correctly captures all of the above enumerated effects. Here, we build upon our work to investigate necessary conditions for comb generation with free-running, self-starting THz QCLs. We performed simulations of a typical resonant phonon THz QCL in regimes of strong and weak SHB. Figures 1(a)-(d) illustrate the former case, when SHB is strong and dominates the mode proliferation process, resulting in an incoherent and chaotically varying spectrum. Next, we simulated a free-running laser with asymmetrically chosen outcoupling losses, where the left reflection coefficient was maintained at 100% and the right one was set to 5%. This strengthens the unidirectionality of the emission and suppresses SHB. The plots in Figs. 1(e)-(h) show that, while keeping all other parameters fixed, by only eliminating spatial hole burning we can recover the comb-like behaviour of the laser. In this configuration, the physics at play strongly resembles the processes in optically pumped high-Q microresonator combs, and so inspired by the work in [6], we also investigate how the relationships between the first modes that start lasing can determine the nature of the radio-frequency beatnote.